How to solve for power in a piano wire wave problem?

In summary: I converted the mass to kg and the length to m. I solved for omega with the equation omega = frequency * 2PI. F I'm assuming is the tension. Then I thought it was simply a plug-in problem, but I can't seem to get it right. I had to do five different trials because at first I solved for μ wrong and then I wasn't sure what units the program wanted it in (just had Watts next to the solution, so I just assumed i needed to put everything into kg and m and all that stuff). But yea, I don't know what I'm doing wrong.
  • #1
DGalt
4
0

Homework Statement


A piano wire with mass 3.25 g and length 84.0 cm is stretched with a tension of 27.0 N. A wave with frequency 100 Hz and amplitude 1.30 mm travels along the wire.


Homework Equations


The only equation that I think applies to this one is P = .5*Sqrt(μ*F)*(omega^2)*A^2


The Attempt at a Solution


I've tried this freaking problem five times now, and I'm down to my last try on Mastering Physics (online homework program).
I thought this was a pretty straightforward problem. I started out solving for μ by basically converting the mass (3.25g) to kg and the length (84cm) to m and then dividing the mass by the length. I solved for omega with the equation omega = frequency * 2PI. F I'm assuming is the tension.

Then I thought it was simply a plug-in problem, but I can't seem to get it right. I had to do five different trials because at first I solved for μ wrong and then I wasn't sure what units the program wanted it in (just had Watts next to the solution, so I just assumed i needed to put everything into kg and m and all that stuff). But yea, I don't know what I'm doing wrong.

If anyone can help me out on this one I'd appreciate it, just can't seem to figure out what went wrong

thanks in advance
 
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  • #2
What's the question?
 
  • #3
woops...yea I'm an idiot
The question is:
Calculate the average power carried by the wave.
 
  • #4
what answers have you tried
 
  • #5
i have the exact same question on my Mastering Physics homework, and I just figured it out. You use that equation and just plug everything in, but the units must be converted for almost everything. So the mass must be in kg, length must be in meters, tension is in N already, frequency is in Hz already, but amplitude must be in meters (not mm). Once you convert everything and plug it into the equation, you get the right answer (mine was about 0.3 W, my numbers may be different than yours though!) For the part B, you just do (1/2) of the amplitude when plugging it in!

Good luck!
 
  • #6
Clarification? what did you change the formula into?
 

1. What is the definition of mechanical waves?

Mechanical waves are a type of wave that requires a medium, such as air or water, to travel through. They are characterized by the transfer of energy through the particles of the medium, causing them to vibrate.

2. How is power related to mechanical waves?

Power is a measure of the rate at which energy is transferred. In the context of mechanical waves, power is directly related to the amplitude of the wave. The higher the amplitude, the more energy is transferred per unit time, resulting in a higher power.

3. What factors affect the power of a mechanical wave?

The power of a mechanical wave is affected by several factors, including the amplitude and frequency of the wave, the density and elasticity of the medium, and the distance the wave travels. The medium's properties play a significant role in determining the power of a wave.

4. How is the power of a mechanical wave measured?

The power of a mechanical wave can be measured using the equation P = E/t, where P is power, E is energy, and t is time. The energy of a wave can be calculated using the equation E = 0.5mv^2, where m is the mass of the medium and v is the velocity of the wave.

5. What is the relationship between power and intensity in mechanical waves?

Power and intensity are directly proportional in mechanical waves. Intensity is a measure of how much energy is transmitted through a given area per unit time. As power increases, intensity also increases, meaning that more energy is being transferred through a smaller area in a shorter amount of time.

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